Cake Pan Converter
Area goes as the square of the diameter, so 8 inch to 9 inch is 27 percent more, not 12.
The formula
scale by the ratio of AREAS, not of diameters
Area, not diameter
Moving a recipe from an 8-inch tin to a 9-inch one is not a 12 % increase. Area goes as the square of the diameter, so it is 27 %, and scaling by the diameter leaves a cake noticeably thin. The same trap catches people going the other way, where the batter overflows.
Depth changes the time, not the quantity
Two tins of equal area but different depth take the same batter and bake differently: the deeper one needs a lower oven and longer, or the outside sets before the middle. A rough guide is that a batter 50 % deeper needs about 25 % longer and 10 degrees cooler.
Round against square
A square tin holds about 27 % more than a round one of the same nominal size, because the corners are extra area. An 8-inch square is close to a 9-inch round, which is the single most useful substitution to remember.
Recipes are starting points
Ovens run hot or cold by 20 degrees, flour absorbs water differently by season and brand, and the same joint of meat cooks at a different rate depending on its shape rather than its weight. Everything here is a planning figure that gets you close enough to start, and the thermometer, the scales and your own notes from last time are what finish the job.